Physics
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufm.p42b..04g&link_type=abstract
American Geophysical Union, Fall Meeting 2007, abstract #P42B-04
Physics
1221 Lunar And Planetary Geodesy And Gravity (5417, 5450, 5714, 5744, 6019, 6250), 5450 Orbital And Rotational Dynamics (1221), 5455 Origin And Evolution, 6250 Moon (1221)
Scientific paper
If taken at face value, the principal lunar moments of inertia suggest that the Moon froze in a past tidal and rotational state during a high eccentricity orbit [1]. At this time the Moon may have been in either synchronous rotation or in a 3:2 resonance of spin and mean motion. We have performed further investigations of the plausibility of past high eccentricity lunar orbits on the basis of orbital evolution, the dynamics of entry into any past 3:2 resonance, and tidal dissipation. We have found that the requisite permanent (B-A)/C (where A, B, and C are the principal moments of inertia) for a 3:2 resonance can be achieved in a magma ocean if a density anomaly is present shortly after lunar accretion. In a high eccentricity orbit, tidal dissipation will affect the Moon's ability to develop lithospheric strength. The Moon is presently able to support degree-two loads, while Io, which is approximately the same size as the Moon and strongly heated by tidal dissipation, probably cannot [2]. Therefore, somewhere between the present lunar radioactive heating rate (~1012 W), and Io's observed dissipation (~1014 W), the Moon may develop lithospheric strength. We use 1014 W as a loose upper bound on where freeze-in may begin and find that in a 3:2 resonance tidal dissipation [3] can drop below 1014 W at a = 25 RE and e = 0.17, and the present moments of inertia can be approximately reproduced for lunar values of QM = 475 (where a is the lunar semimajor axis, RE is the Earth radius, and Q is the specific dissipation function). This value of QM is somewhat large, but the biggest problem with a 3:2 resonance that lasts until 25 RE is how to achieve the current low eccentricity synchronous orbit. The required damping cannot be easily achieved unless the Moon is knocked out of a 3:2 resonance by an impactor that would produce a crater approximately 800 km in diameter. In sum, there is no single strong constraint that completely rules out a 3:2 resonance, but it would require a rather specific set of circumstances. For the high-eccentricity (e = 0.49) synchronous solution to the moments of inertia, we have found that dissipation at e = 0.49 is several orders higher than 1014 W for QM less than 500 and k2 = 1.5 (where k2 is the second degree tidal Love number), and therefore freeze-in during such a scenario is almost completely ruled out (in agreement with Wisdom, unpublished notes). During the magma ocean phase of lunar history it is also possible that the lunar gravity field was too homogeneous to provide a sufficient permanent (B-A)/C for even synchronous rotation. In this case the Moon would achieve an asymptotic spin rate slightly faster than synchronous [4]. If during this very early time in lunar evolution, the Moon froze in even a small amount of its shape, it would be entirely rotational, and provide an alternative explanation for the high relative amount of rotational potential in the present degree-two gravity field. References: [1] Garrick-Bethell, I., Wisdom, J., Zuber, M. T. (2006) Science 313, 652-655. [2] Anderson, J. D. et al. (2001) J. of Geophys. Res. 106, 32963-32970. [3] Wisdom, J. (2007), in press. [4] Peale, S. J.; Gold, T. (1965) Nature 206, 1240.
Garrick-Bethell Ian
Zuber Maria T.
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